Officials inside the Central Intelligence Agency knew that Saudi Arabia was serious about toppling Syrian President Bashar al-Assad when the Saudi king named Prince Bandar bin Sultan al-Saud to lead the effort.

They believed that Prince Bandar, a veteran of the diplomatic intrigues of Washington and the Arab world, could deliver what the CIA couldn't: planeloads of money and arms, and, as one U.S. diplomat put it, wasta, Arabic for...